What Are the Two Possible Launch Angles for a Ball to Land 5 Meters Away?

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Homework Help Overview

The problem involves determining the two possible launch angles for a ball that is projected at a speed of 10 m/s and lands 5 meters away. The context is rooted in projectile motion and the equations governing it.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss setting up equations of motion to relate time and distance, questioning how to express the initial velocity in terms of horizontal and vertical components. There is an emphasis on understanding the relationship between these components and the trajectory.

Discussion Status

Some participants have offered insights into constructing equations for the horizontal and vertical motions, while others express confusion about how to decompose the initial velocity into its components. Multiple interpretations of the problem setup are being explored.

Contextual Notes

There is a reference to external resources for further understanding, indicating that participants may be looking for additional context or clarification on the topic of projectile motion.

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Homework Statement


A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal.


Homework Equations


The equations of motion.


The Attempt at a Solution


I realize that I need to find the angle θ and then use sin(180-θ) to find the other possible angle however I do not know how to get it.
 
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Interesting problem.

What I'd do is set up a system of equations. You know that the time it takes for the ball the fall and the time it takes for the ball to travel 5 m is the same, right? So, build two position equations and solve for t, then set them equal to each other, leaving only one variable, your angle.

Keeping the angle as a variable, theta, can you come up with two functions, one for the y position and one for the x position? What should the values of these functions as a whole be for each one?

What part of the 10 m/s is horizontal? Which part of the 10 m/s is vertical?
 
What I don't understand is how to split to 10m/s into hortizontal and vertical components in order to get the time.
 
10 meters per second is the magnitude of the vector. Its the same concept as the hypotenuse of a triangle.
 
jumbo123 said:

Homework Statement


A ball is launched at a speed of 10ms-1. It lands 5m away. Find the two possible values of the angle, θ, which the initial trajectory makes with the horizontal.


Homework Equations


The equations of motion.


The Attempt at a Solution


I realize that I need to find the angle θ and then use sin(180-θ) to find the other possible angle however I do not know how to get it.

jumbo123 said:
What I don't understand is how to split to 10m/s into hortizontal and vertical components in order to get the time.

See the "Range and Height" figure at this introductory page:

http://en.wikipedia.org/wiki/Trajectory

.
 

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